基于NURBS曲面拟合的三角网格曲率计算

针对三角网格提出了一种基于NURBS曲面拟合的计算Gauss曲率和平均曲率的算法。首先选取边界检测后的二阶邻点作为局部拟合数据,采用直接投影法实现参数化,由二次NURBS曲面进行最小平方拟合反算控制点矩阵,最后由拟合曲面计算曲率。并从三角网格分辨率和噪声两方面进行了比较,实验结果表明本文算法精度高、较其他算法稳定,因而更具通用性。     

Curvature estimation scheme for triangle meshes using biquadratic Bézier patches

When dealing with triangle meshes, it is often important to compute curvature information for the purposes of feature recognition, segmentation, or shape analysis. Since a triangle mesh is a piecewise linear surface, curvature has to be estimated. Several different schemes have been proposed, both discrete and continuous, i.e. based on fitting surfaces locally. This paper compares commonly used discrete and continuous curvature estimation schemes. We also present a novel method which uses biquadratic Bézier patches as a local surface fitting technique.     

基于法线网格的渐进压缩

多分辨率分析(Multi resolutionAnalysis)和法线网格(Normalmeshes)是近年来进行三维网格图形处理和网格压缩的新方法。该文在这两项技术的基础上,提出并实现了三维网格的多分辨率分析及其渐进几何压缩(ProgressiveGeometryCompression)方案, 研究了基于细分的法线网格在多分辨率分析中的边界处理问题。实验结果表明,利用法线网格的多分辨率分析结合法向多边形构造方法来处理边界,可以取得非常高的压缩率和较好的重构效果。     

Curvature continuous interpolation of curve meshes

This paper presents a method for local construction of a curvature continuous (GC²) piecewise polynomial surface which interpolates a given rectangular curvature continuous quintic curve mesh. First, we create a C² quintic basic curve mesh, which interpolates the same grid points, preserves the tangent slopes and curvatures but not derivative vectors at the grid points. After estimating twist and higher order mixed partial derivatives for each grid point, we generate locally the so-called C² biquintic basic patches, which serve to compute the first and second order cross-derivative functions of the final interpolation surface. In order to match the tangents and second order derivative vectors of the original boundary curves at the grid points, these basic patches are reparametrized by 5 × 3 and 3 × 5 functions, which lead to vector-valued first and second order cross-derivative functions of degrees 7 and 9 of the final surface patches, and eventually lead to a GC² piecewise polynomial surface of degree 9 × 9, which is then converted to a GC² Bézier composite surface. By arranging the surface patches in a chess-board fashion, the degrees of the final surface patches can be 9 × 5 and 5 × 9. An example for the construction of a GC² ship hull, together with its color-coded curvature maps, is given to illustrate the method. This method is attractive because the final surface has a much lower degree than other similar methods, it allows flexible local modification of the original curve mesh and local editing of the interpolation surface, and it is easily integrated into state-of-the-art geometric modeling systems.     

散乱点云数据曲率估计方法

针对带有强噪声离散点云数据曲率计算问题,提出一种基于稳健统计的曲率估计方法。首先,用一个二次曲面拟合三维空间采样点处的局部形状;其次,随机地选择该采样点邻域内的子集,多次执行这样的拟合过程,通过变窗宽的最大核密度估计,就得到了最优拟合曲面;最后,将采样点投影到该曲面上,计算投影点曲率信息,就得到采样点曲率。实验结果表明,所提方法对噪声和离群点是稳健的,特别是随着噪声方差的增大,要明显好于传统的抛物拟合方法。     

基于正态区间估计的改进型无量纲化方法

针对综合评价指标无量纲化问题,现有方法虽然考虑了评价的实际需要,但没有考虑评价值异常点对综合评价的影响,以致可能出现某个评价值异常性较大,而导致评价错误的结果。提出了一种基于正态区间估计的改进型无量纲化方法,利用正态区间估计的方法给出异常评价值的定义规则和处理规则,按照规则对评价值异常点进行辨识和修正,采用标准化方法对评价值进行无量纲化,提高评价值之间的区分度。经算例分析表明,该方法可行有效。     

Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes

We extend the error analysis of Adjerid and Baccouch [1], [2] for the discontinuous Galerkin discretization error to variable-coefficient linear hyperbolic problems as well as nonlinear hyperbolic problems on unstructured meshes. We further extend this analysis to transient hyperbolic problems and prove that the local superconvergence results presented in [1] still hold for both steady and transient variable-coefficient linear and nonlinear problems. This local error analysis allows us to construct asymptotically correct a posteriori error estimates by solving local hyperbolic problems with no boundary conditions on each element of general unstructured meshes. We illustrate the superconvergence and the efficiency of our a posteriori error estimates by showing computational results for several linear and nonlinear numerical examples.     

A comparison of algorithms for vertex normal computation

We investigate current vertex normal computation algorithms and evaluate their effectiveness at approximating analytically computable (and thus comparable) normals for a variety of classes of model. We find that the most accurate algorithm depends on the class and that for some classes, none of the available algorithms is particularly good. We also compare the relative speeds of all algorithms.     

三角网格曲面上离散曲率改进算法

计算三角网格离散曲面曲率的Meyer方法几何意义简明,计算量较小,但其计算效果仍有进一步提高的潜力。通过对Meyer方法的深入分析,提出了平均曲率构造向量和Gauss曲率构造角的概念,并指出了它们的几何意义,在此基础上构造了对Meyer方法的改进算法。经分析,提出的改进算法精简了各个主要计算步骤,避免了不必要的计算误差。仿真计算结果表明,改进算法是有效的,提高了三角网格离散曲率的计算精度和计算效率。     

A comparison of gradient estimation methods for volume rendering on unstructured meshes

This paper presents a study of gradient estimation methods for rendering unstructured-mesh volume data. Gradient estimation is necessary for rendering shaded isosurfaces and specular highlights, which provide important cues for shape and depth. Gradient estimation has been widely studied and deployed for regular-grid volume data to achieve local illumination effects, but has been, otherwise, for unstructured-mesh data. As a result, most of the unstructured-mesh volume visualizations made so far were unlit. In this paper, we present a comprehensive study of gradient estimation methods for unstructured meshes with respect to their cost and performance. Through a number of benchmarks, we discuss the effects of mesh quality and scalar function complexity in the accuracy of the reconstruction, and their impact in lighting-enabled volume rendering. Based on our study, we also propose two heuristic improvements to the gradient reconstruction process. The first heuristic improves the rendering quality with a hybrid algorithm that combines the results of the multiple reconstruction methods, based on the properties of a given mesh. The second heuristic improves the efficiency of its GPU implementation, by restricting the computation of the gradient on a fixed-size local neighborhood.     

基于渐进网格的复杂模型简化算法

在某些应用领域中,常会遇到一些较为复杂的模型。处理这些模型时,在显示、硬件需求等方面会遇到些困难。为了缓解这些困难,阐述了一种基于渐进网格的简化方法。经过多分辨率分解之后,复杂模型被表示为一个低分辨率网格,同时记录下相关的细节。通过该方法,可以很好地简化复杂模型以满足用户的需求并且效率也能被提高。     

基于非结构网格的Gas-Kinetic方法

为解决带有复杂几何边界条件的高速流体计算问题,提出基于非结构网格的Gas-Kinetic方法.对于二维非结构网格,以三角形网格作为计算单元,形成在该网格控制单元中物理量导数求解的新方法.通过物理量导数得到在控制体积元边界上的通量,然后用每个计算时间步中求出的边界通量和控制体积元中的物理量,求出下一计算时间步所需的新物理量,依次进行计算直到计算结果收敛为止.采用NACA0012翼型进行数值计算验证,结果表明该方法简单高效,适用于低速和高速流体的计算.     

An auxiliary gaze point estimation method based on facial normal

Considering the main disadvantage of the existing gaze point estimation methods which restrict user’s head movement and have potential injury on eyes, we propose a gaze point estimation method based on facial normal and binocular vision. Firstly, we calibrate stereo cameras to determine the extrinsic and intrinsic parameters of the cameras; Secondly, face is quickly detected by Viola–Jones framework and the center position of the two irises can be located based on integro-differential operators; The two nostrils and mouth are detected based on the saturation difference and their 2D coordinates can be calculated; Thirdly, the 3D coordinates of these five points are obtained by stereo matching and 3D reconstruction; After that, a plane fitting algorithm based on least squares is adopted to get the approximate facial plane, then, the normal via the midpoint of the two pupils can be figured out; Finally, the point-of-gaze can be obtained by getting the intersection point of the facial normal and the computer screen. Experimental results confirm the accuracy and robustness of the proposed method.     

基于三角形外接圆的轮廓对应算法

针对目前的轮廓对应算法在处理形状复杂的研究对象时容易产生错误的对应关系及计算效率低的问题,提出了基于三角形外接圆的轮廓对应算法。该算法对位于不同截面上的每一个轮廓进行三角剖分,将剖分得到的三角形合法化之后提取其外接圆,通过研究位于相邻截面上的外接圆间的对应关系来确定轮廓间的对应。实验结果表明,该算法能够很好地处理形状复杂的研究对象,具有较好的鲁棒性和实时性。     

曲面的有限元网格顶点法矢算法

分析计算有限元三角形网格顶点法矢的各种算法原理,比较各种算法的结果精度,指出Max方法考虑了三角形网格的形状,且本质上是一种通过对四面体进行外接球面拟合的计算方法,结果精度很高.在此基础上,针对曲面在有限元网格划分后可能同时存在三角形网格和四边形网格,提出适应于单独的三角形网格和四边形网格与两者并存的混合网格的顶点法矢求取算法,计算结果表明了算法的适应性和有效性.     

基于顶点度的模型简化算法

针对基于二次误差度量的边收缩算法在计算大度顶点误差度量时计算量大,且收缩该类顶点关联边时易使关键点发生偏移而引起模型变动过大、简化不够准确的问题,提出了基于顶点度的模型简化算法.该算法不但提高了模型的简化质量,而且加快了模型的简化速度.     

A posteriori error estimation for the heterogeneous Maxwell equations on isotropic and anisotropic meshes

We consider residual-based a posteriori error estimators for the heterogeneous Maxwell equations using isotropic as well as anisotropic meshes. The continuous problem is approximated by using conforming approximated spaces with minimal assumptions. Lower and upper bounds are obtained under standard assumptions on the meshes. The lower bound holds unconditionally, while the upper bound depends on alignment properties of the meshes with respect to the solution. In particular for isotropic meshes the upper bound also holds unconditionally. A numerical test is presented which confirms our theoretical results.     

Parametric estimation for normal mixtures

Described here are two approaches for estimating the parameters (a-priori probabilities, means, and covariances) of a mixture of normal distributions, given a finite sample X drawn from the mixture. One approach is based on a modification of the EM algorithm for computing maximum-likelihood estimates, while the other makes use of the Fuzzy c-Means algorithms for locating clusters. The reliability, accuracy, and efficiency of these two algorithms are compared using samples drawn from three artificial univariate normal mixtures of two classes.     

基于3DS模型的四边形网格生成算法研究

针对文献[1]中提出的四边形网格形变因子的不足,提出了曲面中改进的四边形形变因子。根据此约束条件,研究并实现了一种将3DS模型表面三角形网格转化为四边形网格的合并算法,并对极少的残余三角形进行拆分处理,实现彻底转化。经过对已有模型的实际转化实验,表明了本算法的有效性。